No, the terminology sounds right to me. The term front-end and back-end are used in other contexts than building websites.
For example, the term is used in compilers, where the front-end takes code in a programming language and translates it to an intermediate representation (IR), and the back-end takes the IR and translates that into machine code for a specific architecture. A compiler like LLVM has many front-ends and back-ends to support different languages and architectures.
The term applies to many things where there is a multi-layered architecture.